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12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Two

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

    (a)

    \(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) A\)

    (b)

    \(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) { A }^{ T }\)

    (c)

    \(\left( \cos ^{ 2 }{ \theta } \right) I\)

    (d)

    (Sin2\(\frac { \theta }{ 2 } \))A

  2. If \(\rho\)(A) = r then which of the following is correct?

    (a)

    all the minors of order n which do not vanish

    (b)

    'A' has at least one minor "of order r which does not vanish and all higher order minors vanish

    (c)

    'A' has at least one (r + 1) order minor which vanish

    (d)

    all (r + 1) and higher order minors should not vanish

  3. In the system of liner equations with 3 unknowns If \(\rho\)(A) = \(\rho\)([A|B]) =1, the system has ________

    (a)

    unique solution

    (b)

    inconsistent

    (c)

    consistent with 2 parameter -family of solution

    (d)

    consistent with one parameter family of solution.

  4. The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

    (a)

    \(\cfrac { 1 }{ 2 } \left| z \right| ^{ 2 }\)

    (b)

    |z|2

    (c)

    \(\cfrac { 3 }{ 2 } \left| z \right| ^{ 2 }\)

    (d)

    2|z|2

  5. If z = a + ib lies in quadrant then \(\frac { \bar { z } }{ z } \) also lies in the III quadrant if

    (a)

    a > b > 0

    (b)

    a < b < 0

    (c)

    b < a < 0

    (d)

    b > a > 0

  6. If ax2 + bx + c = 0, a, b, c E R has no real zeros, and if a + b + c < 0, then __________

    (a)

    c>0

    (b)

    c<0

    (c)

    c=0

    (d)

    c≥0

  7. The value of \({ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right) \) is 

    (a)

    \(\cfrac { \pi }{ 2 } \)

    (b)

    \(\cfrac { 5\pi }{ 3 } \)

    (c)

    \(\cfrac { 10\pi }{ 3 } \)

    (d)

    0

  8. The pricipal value of \({ sin }^{ -1 }\left( \cfrac { -1 }{ 2 } \right) \) is _________

    (a)

    \(\cfrac { \pi }{ 6 } \)

    (b)

    \(\cfrac { -\pi }{ 6 } \)

    (c)

    \(\cfrac { \pi }{ 3 } \)

    (d)

    \(\cfrac { -\pi }{ 3 } \)

  9. Angle between y2 = x and.x2= y at the origin is

    (a)

    \({ tan }^{ -1 }\cfrac { 3 }{ 4 } \)

    (b)

    \({ tan }^{ -1 }\left( \cfrac { 4 }{ 3 } \right) \)

    (c)

    \(\cfrac { \pi }{ 2 } \)

    (d)

    \(\cfrac { \pi }{ 4 } \)

  10. Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k2 , where k is the face that comes up k = {1, 2, 3, 4, 5}.
    The expected amount to win at this game in Rs. is

    (a)

    \(\cfrac { 19 }{ 6 } \)

    (b)

    \(-\cfrac { 19 }{ 6 } \)

    (c)

    \(\cfrac { 3 }{ 2 } \)

    (d)

    \(-\cfrac { 3 }{ 2 } \)

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